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Differential Calculus> Find the interval in which f(x) is increa...

question mark

Find the interval in which f(x) is increasing
f(x) = ∫e^x(x-1)(x-2) dx
Limit is from 0 to x.

Lovey , 10 Years ago

Grade 12

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:
Hello Student,
Please find answer to your question below

$f(x) = \int_{0}^{x}e^{t}(t-1)(t-2)dt$
Using Newton-Leibniz formula, we have
$f'(x) = e^{x}(x-1)(x-2)$
f(x) is increasing in the interval
$f'(x)$ > 0
$e^{x}(x-1)(x-2)$ > 0
e^xis always +ve for all x.
$(x-1)(x-2)$ > 0
By wavy crve method, we have
$x\in R - [1, 2]$

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